Consider Model 1 in Table 6. The dependent variable is “% increase in number of private sector employees (2001-2006)” and the independent variable is “Local university presence”. The estimated coefficient on "Local university presence" is 0.27 with a standard error of 0.11. Which of the following is true? (note the critical values for a 10% significance test are -1.645 and 1.645)

Question

Consider Model 1 in Table 6. The dependent variable is “% increase in number of private sector employees (2001-2006)” and the independent variable is “Local university presence”. The estimated coefficient on "Local university presence" is 0.27 with a standard error of 0.11. Which of the following is true? (note the critical values for a 10% significance test are -1.645 and 1.645)

BlackTom AI · Accepted Answer

The question asks us to evaluate the statistical significance of the slope coefficient on Local university presence, given a coefficient of 0.27 and a standard error of 0.11, with a 10% significance test critical value of ±1.645.
Option 1: 'The slope coefficient estimate is statistically significantly different from zero at the 0.10% level of significance.' To assess this, compute the test statistic t = 0.27 / 0.11 ≈ 2.455. A 0.10% (very stringent) test would require a much larger magnitude than 1.645, so this statement is not supported by the data. It overstates the evidence against zero.
Option 2: 'The intercept coefficient estimate is statistically significantly different from zero at the 10% level of significance.' The information provided gives the slope and its standard error, not the intercept or its standard error. Without the intercept’s estimate and standard error, we cannot conclude anything about it. This claim cannot be evaluated as true from the given data.
Option 3: 'The slope coefficient estimate is not statistically significantly different from zero at the 10% level of significance.' Given t ≈ 2.455 and the 10% critical value 1.645, the absolute t-statistic exceeds the critical value, indicating statistical significance at the 10% level. Therefore, this statement is contradicted by the calculation.
Option 4: 'The slope coefficient estimate is statistically significantly different from zero at the 10% level of significance.' As shown, |t| ≈ 2.455 > 1.645, which means the null hypothesis that the slope is zero would be rejected at the 10% level. This aligns with the standard interpretation of a t-test for a single coefficient when |t| exceeds the critical value.
In summary, the key steps involve forming the t-statistic from the given coefficient and its standard error, comparing its magnitude to the critical value for the specified significance level, and applying the decision rule: if |t| > critical, reject the null hypothesis of zero slope at that level. Remember that options about the intercept cannot be judged from the provided slope data, and claims about extremely small p-values require correspondingly larger test statistic values than 1.645.

ECON1272 Quiz 2 - Basic Econometrics

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